Alge-Tiles an Overview.

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Alge-Tiles an Overview

x Set 1 1 x2 Set 2 xy y2 y

x – x = 0 –1 1 x2 – x2 xy y2 –y2 – xy y – y

Adding Integers (+ 5) (+ 7) + = 12

Adding Integers (– 5) + (– 7) + = – 12

Adding Integers (– 5) = + 3

Subtracting Integers (– 2) – (– 4) + = 2

Subtracting Integers (– 4) – (+ 6) + = – 10

Multiplying Integers 6 (2)(3) –6 (2)(–3) (–2)(–3) 6

Algebraic Expressions
x2 + 2x + 4 x2 – 3x – 2 2x2 – x + 2

Adding Polynomials (4x + 5) + (2x – 3) + = 6x + 2

Subtracting Polynomials
(5x + 2) – (3x – 4) + = 2x + 6

Multiplying Polynomials
3(x + 2) x + 2 3 Guiding tiles

Multiplying Polynomials
3(x + 2) 3x + 6

Multiplying Polynomials
x(x – 3) x – 3 x Guiding tiles

Multiplying Polynomials
x(x – 3) x2 – 3x

Multiplying Polynomials
(x + 2)(x + 3) x + 2 x + 3 Guiding tiles

Multiplying Polynomials
(x + 2)(x + 3) x2 + 5x + 6

Multiplying Polynomials
(x – 2)(x + 2) x – 2 x + 2

Multiplying Polynomials
(x – 2)(x + 2)

Multiplying Polynomials
(x – 2)(x + 2) x2 – 4

Factoring Polynomials
x2 + 6x + 8 x + 4 x + 2 Form a rectangle x2 + 6x + 8 = (x + 2)(x + 4)

Solving Equations: solve for x

Solving Equations: solve for x

Solving Equations: solve for x

Solving Equations: solve for x

Solving Equations: solve for x

Solving Equations: solve for x
3x – 1 = x – 5

Solving Equations: solve for x
3x – 1 = x – 5

Solving Equations: solve for x
3x – 1 = x – 5 x = –2

Both sides have seven white tiles.
Check Substitute for 3x – 1 = x – 5 x = –2 Both sides have seven white tiles.